SECTION VIII. 



FORMATION OF THE EQUATIONS OF CONDITION, FORMATION OF THE 

 FINAL EQUATIONS AND THE DETERMINATION OF THE VALUES OF 

 THE MAGNETIC CONSTANTS. 



1. THE theory of Terrestrial Magnetism, as developed in Section V. 

 for the Sphere, and in Section VI. for the Spheroidal surface, requires 

 that the observations of the horizontal and vertical magnetic forces should 

 be distributed uniformly over the whole surface of the Earth. In the 

 absence of such observations, and especially when as yet there are very 

 few trustworthy observations of the magnetic elements taken in high 

 latitudes, it is necessary to adopt some other method of solution of the 

 equations of condition just given at the end of the preceding Section, 

 taking only those equations which relate to that portion of the Earth's 

 surface over which fairly good observations have been taken. Under these 

 circumstances it will be necessary to take into account the values of 

 those terms of the equations which now no longer vanish when the 

 integration is not taken over the whole surface of the Earth. We will 

 assume that the Charts from which the observations are taken are trust- 

 worthy up to a latitude of 67 either north or south of the Equator, 

 i.e. taking a central belt 5 broad at the Equator and 13 belts of the 

 same breadth on either side of it. 



The equations of condition given in Section VII. and the final 

 equations for X, Y and Z for the period 1845 are formed for each belt 

 between latitudes 77|N. and 77| S., i.e. for 15 belts of 5 on either 

 side of the equatorial belt, but the observations in extreme northern or 

 southern latitudes between 67 and 77 have not been included in the 

 solution of the equations except in a few special instances. 



